A Pareto-metaheuristic for a bi-objective winner determination problem in a combinatorial reverse auction

The bi-objective winner determination problem (2WDP-SC) of a combinatorial procurement auction for transport contracts comes up to a multi-criteria set covering problem. We are given a set B of bundle bids. A bundle bid b in B consists of a bidding carrier c_b, a bid price p_b, and a set tau_b of transport contracts which is a subset of the set T of tendered transport contracts. Additionally, the transport quality q_t,c_b is given which is expected to be realized when a transport contract t is executed by a carrier c_b. The task of the auctioneer is to find a set X of winning bids (X is subset of B), such that each transport contract is part of at least one winning bid, the total procurement costs are minimized, and the total transport quality is maximized. This article presents a metaheuristic approach for the 2WDP-SC which integrates the greedy randomized adaptive search procedure, large neighborhood search, and self-adaptive parameter setting in order to find a competitive set of non-dominated solutions. The procedure outperforms existing heuristics. Computational experiments performed on a set of benchmark instances show that, for small instances, the presented procedure is the sole approach that succeeds to find all Pareto-optimal solutions. For each of the large benchmark instances, according to common multi-criteria quality indicators of the literature, it attains new best-known solution sets.Pareto optimization; multi-criteria winner determination; combinatorial auction; GRASP; LNS

Approach of Genetic Algorithms With Grouping Into Species Optimized With Predator-Prey Method for Solving Multimodal Problems

[Abstract] Over recent years, Genetic Algorithms have proven to be an appropriate tool for solving certain problems. However, it does not matter if the search space has several valid solutions, as their classic approach is insufficient. To this end, the idea of dividing the individuals into species has been successfully raised. However, this solution is not free of drawbacks, such as the emergence of redundant species, overlapping or performance degradation by significantly increasing the number of individuals to be evaluated. This paper presents the implementation of a method based on the predator-prey technique, with the aim of providing a solution to the problem, as well as a number of examples to prove its effectiveness

An Application of Self-Organizing Map for Multirobot Multigoal Path Planning with Minmax Objective

In this paper, Self-Organizing Map (SOM) for the Multiple Traveling Salesman Problem (MTSP) with minmax objective is applied to the robotic problem of multigoal path planning in the polygonal domain. The main difficulty of such SOM deployment is determination of collision-free paths among obstacles that is required to evaluate the neuron-city distances in the winner selection phase of unsupervised learning. Moreover, a collision-free path is also needed in the adaptation phase, where neurons are adapted towards the presented input signal (city) to the network. Simple approximations of the shortest path are utilized to address this issue and solve the robotic MTSP by SOM. Suitability of the proposed approximations is verified in the context of cooperative inspection, where cities represent sensing locations that guarantee to “see” the whole robots’ workspace. The inspection task formulated as the MTSP-Minmax is solved by the proposed SOM approach and compared with the combinatorial heuristic GENIUS. The results indicate that the proposed approach provides competitive results to GENIUS and support applicability of SOM for robotic multigoal path planning with a group of cooperating mobile robots. The proposed combination of approximate shortest paths with unsupervised learning opens further applications of SOM in the field of robotic planning

Approach for solving multimodal problems using Genetic Algorithms with Grouped into Species optimized with Predator-Prey

Over recent years, Genetic Algorithms have proven to be an appropriate tool for solving certain problems. However, it does not matter if the search space has several valid solutions, as their classic approach is insufficient. To this end, the idea of dividing the individuals into species has been successfully raised. However, this solution is not free of drawbacks, such as the emergence of redundant species, overlapping or performance degradation by significantly increasing the number of individuals to be evaluated. This paper presents the implementation of a method based on the predator-prey technique, with the aim of providing a solution to the problem, as well as a number of examples to prove its effectiveness